y^'+2xy=e^x

Lösung

y^{^{'}} + 2 x y = e^{x}

y = \frac{π erfi ( x + \frac{1}{2} ) e ^{\frac{1 - 4 x ^{2}}{4}}}{2} + \frac{c _{1}}{e ^{x^{2}}}

Schritte zur Lösung

y^{'} (x) + 2 x y = e^{x}

Solve linear ODE:

y = \frac{π erfi ( x + \frac{1}{2} ) e ^{\frac{1 - 4 x ^{2}}{4}}}{2} + \frac{c _{1}}{e ^{x^{2}}}

y = \frac{π erfi ( x + \frac{1}{2} ) e ^{\frac{1 - 4 x ^{2}}{4}}}{2} + \frac{c _{1}}{e ^{x^{2}}}

x \to - 6 lim (x + 1)

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